Substitute Richard Cresswell missed the best chance of the first half
Fulham remain without an away win in the Premier League this season after neither side could find a cutting edge.
Stoke lost Mamady Sidibe through injury in the opening moments, and Rory Delap later aggravated a shoulder injury and so could not take his dangerous throws.
Fulham had good quality possession and saw penalty claims ignored but Stoke substitute Richard Cresswell had the best chance, firing over from 15 yards.
Simon Davies shot wide for the visitors after the break but a draw was fair.
Stoke, with victories over Tottenham and Arsenal at the Britannia Stadium already this season and unbeaten in their last five home league matches, would have been confident of improving that record given Fulham's lack of goals on their travels.
But their plans were soon disrupted when Sidibe was stretchered off after falling awkwardly in the opening seconds.
To make matters worse, long-throw specialist Delap, who had passed a fitness test on his troublesome shoulder, appeared to aggravate it when he tried to launch one into the area and the ball went only a few feet in front of him.
Fulham, by contrast, were quickly into their stride and played some attractive stuff, with Danny Murphy and Jimmy Bullard influential.
Andy Johnson, playing as a lone striker in the absence of the injured Bobby Zamora, was infuriated as two penalty claims were rejected in a matter of moments.
Firstly, he fell under a challenge from Glenn Whelan on the edge of the area, and then Danny Higginbotham seemed to clearly handle a Bullard cross from the right.
Hodgson has 'no doubt' about penalty
Neither claim was given by young referee Stuart Attwell, the official in charge for the infamous 'ghost goal' at Watford, who was subjected to persistent criticism from players, fans and management.
Stoke had the only clear chance of the first half when substitute Cresswell curled over from 15 yards having been neatly put through by Ricardo Fuller.
Johnson was fortunate not to receive a card for a reckless challenge, while Fuller and John Pantsil both escaped following an ugly head-to-head clash, after which the Fulham man threw himself theatrically to the ground.
Pantsil went straight down the other end to powerfully flick a header towards goal from a free-kick and Stoke keeper Thomas Sorenson was relieved it went straight at him.
Cresswell sliced a left-footed effort well wide as Stoke pressed but Fulham continued to look the more creative going forward.
Pericard burst clear but fans in the back rows were in more danger than Mark Schwarzer as the wild shot skewed high and wide.
Pulis pleased with performance
Stoke manager Tony Pulis: "It was a hard earned point, we had to make four big changes and our lads worked extremely hard.
"Fulham are a decent side and we restricted them to long range shots and had the best chance ourselves. If we'd scored it would have been different."
[both teams had penalty claims rejected] "I'm delighted it wasn't given, I don't think ours was a penalty but I think theirs was."
Fulham boss Roy Hodgson:
"Before the game I'd have been pleased with a point but when you play as well as we did you've got to win.
"Credit to Stoke, they defended with gusto and determination but when you play as well as that and don't win - that's what I'm disappointed about.
"So many times we passed very well and I was expecting us to score but we couldn't find that last pass or shot."
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